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Simplifying 2w2 + 5w + -21 = w2 + 9 Reorder the terms: -21 + 5w + 2w2 = w2 + 9 Reorder the terms: -21 + 5w + 2w2 = 9 + w2 Solving -21 + 5w + 2w2 = 9 + w2 Solving for variable 'w'. Reorder the terms: -21 + -9 + 5w + 2w2 + -1w2 = 9 + w2 + -9 + -1w2 Combine like terms: -21 + -9 = -30 -30 + 5w + 2w2 + -1w2 = 9 + w2 + -9 + -1w2 Combine like terms: 2w2 + -1w2 = 1w2 -30 + 5w + 1w2 = 9 + w2 + -9 + -1w2 Reorder the terms: -30 + 5w + 1w2 = 9 + -9 + w2 + -1w2 Combine like terms: 9 + -9 = 0 -30 + 5w + 1w2 = 0 + w2 + -1w2 -30 + 5w + 1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 -30 + 5w + 1w2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 5w + 30 + w2 = 0 + 30 Reorder the terms: -30 + 30 + 5w + w2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 5w + w2 = 0 + 30 5w + w2 = 0 + 30 Combine like terms: 0 + 30 = 30 5w + w2 = 30 The w term is 5w. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5w + 6.25 + w2 = 30 + 6.25 Reorder the terms: 6.25 + 5w + w2 = 30 + 6.25 Combine like terms: 30 + 6.25 = 36.25 6.25 + 5w + w2 = 36.25 Factor a perfect square on the left side: (w + 2.5)(w + 2.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (w + 2.5) equal to 6.020797289 and -6.020797289.Subproblem 1
w + 2.5 = 6.020797289 Simplifying w + 2.5 = 6.020797289 Reorder the terms: 2.5 + w = 6.020797289 Solving 2.5 + w = 6.020797289 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + w = 6.020797289 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + w = 6.020797289 + -2.5 w = 6.020797289 + -2.5 Combine like terms: 6.020797289 + -2.5 = 3.520797289 w = 3.520797289 Simplifying w = 3.520797289Subproblem 2
w + 2.5 = -6.020797289 Simplifying w + 2.5 = -6.020797289 Reorder the terms: 2.5 + w = -6.020797289 Solving 2.5 + w = -6.020797289 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + w = -6.020797289 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + w = -6.020797289 + -2.5 w = -6.020797289 + -2.5 Combine like terms: -6.020797289 + -2.5 = -8.520797289 w = -8.520797289 Simplifying w = -8.520797289Solution
The solution to the problem is based on the solutions from the subproblems. w = {3.520797289, -8.520797289}
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